Sherwood studied under legendary acting coach Lee Strasberg at the Actors Studio in New York. She made her Broadway debut in 1952 in The Chase,originating the role of the accuser Abigail Williams in Arthur Miller's canonical play The Crucible. Sherwood herself was blacklisted during this time, which made the play - The Crucible uses the Salem witch trials as an allegory for the McCarthy hearings - particularly personal. In the '60s, she was active in the civil rights movement and was arrested while protesting in Alabama.

She was also in the original Elia Kazan-directed Broadway production of Cat on a Hot Tin Roof, playing Mae, and reprised the role in the 1958 film adaptation. Her other Broadway credits included Camelot,The Night of the Iguana and All Over.